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Two vectors having equal magnitudes A make an angle `theta` with eahc other. Find the magnitude and direction of the resultant. |
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Answer» The magnitude of the resultant will be ` B= sqrt(A^2+A^2+2A.A cos theta)` `sqrt(2A^2(1+costheta)= sqrt(4A^2cos^2 theta/2)` ` 2A cos theta/2` The resultant will make an angle `alpha ` with the first vector where `tan alpha= (A sintheta)/(A + A costheta)=(@A sin theta/2 cos theta/2)/(2A cos^2 theta/2)=tan theta/2` or, ` alpha= theta/2` Thus, the resultant of two equal vectors bisects the angle between them. |
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